How to fix the connected edge problem?
You have to check "Merge" And also "First and Last" in the array modifier. You can tweak the merge distance if there is still a gap. Your relative distance should be 1.00 on the array axis for it to work out of the box.

Alternatively, with Blender 2.82 and onward, you can use the weld modifier and set the distance threshold accordingly. This modifier merges vertices which are closer than the threshold.